Completely multiplicative functions with sum zero over generalised prime systems

Neamah, A. A. (2020) Completely multiplicative functions with sum zero over generalised prime systems. Research in Number Theory, 6 (4). 45. ISSN 2363-9555 doi: 10.1007/s40993-020-00215-z

Abstract/Summary

CMO functions multiplicative functions f for which ∑n=1∞f(n)=0. Such functions were first defined and studied by Kahane and Saïas [14]. We generalised these to Beurling prime systems with the aim to investigate the theory of the extended functions and we shall call them CMOP functions. We give some properties and find examples of CMOP functions. In particular, we explore how quickly the partial sum of these classes of functions tends to zero with different generalised prime systems. The findings of this paper may suggest that for all CMOP functions f over N with abscissa 1, we have ∑n≤xn∈Nf(n)=Ω(1x).

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/94202
Identification Number/DOI	10.1007/s40993-020-00215-z
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Research, Beurling’s generalized primes, Multiplicative functions, 11N80, 11N56
Publisher	Springer
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